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MEN OF ItATHEMATICS

make reasonable the hypothesis of the acute angle. The surface
looks like two infinitely long trumpets soldered together at their
largest ends. To describe it more accurately we must introduce
the plane curve called the tractrix, which is generated as follows.

Let two lines XQX', YOY' be drawn hi a horizontal plane
intersecting at right angles in 0, as in Cartesian geometry.
Imagine an inextensible fibre lying along YOY', to one end of
which is attached a small heavy pellet; the other end of the
fibre is at 0. Pull this end out along the line OX. As the pellet

Y

follows, it traces out one half of the tcactrix; the other half is
traced out by drawing the end of the fibre along OX', and of
course is merely the reflection or image in OY of the first half.
The drawing out is supposed to continue indefinitely - Ho
834